## Abstract

The decision time of an infinite time algorithm is the supremum of its halting times over all real inputs. The decision time of a set of reals is the least decision time of an algorithm that decides the set; semidecision times of semidecidable sets are defined similarly. It is not hard to see that ω

1 is the maximal decision time of sets of reals. Our main results determine the supremum of countable decision times as σ and that of countable semidecision times as τ, where σ and τ denote he suprema of Σ1and Σ2- definable ordinals, respectively, over Lω1. We further compute analogous suprema for singletons.

1 is the maximal decision time of sets of reals. Our main results determine the supremum of countable decision times as σ and that of countable semidecision times as τ, where σ and τ denote he suprema of Σ1and Σ2- definable ordinals, respectively, over Lω1. We further compute analogous suprema for singletons.

Original language | English |
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Pages (from-to) | 197-212 |

Number of pages | 16 |

Journal | Notre Dame Journal of Formal Logic |

Volume | 63 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 May 2022 |